The above presents the essential idea for simulating the non-Hermitian systems based on the stochastic Schrödinger equation. This method is fundamentally different from that applied in the previous experiments [1]}, [2]} using auxiliary qubits, where the non-Hermiticity is obtained from a Hermitian Hamiltonian in the extended Hilbert space by tracing the auxiliary degrees of freedom and careful designs of the quantum circuit with complex unitary operations are required [3]}, [4]}. In contrast, our temporal average approach based on the stochastic Schrödinger equation saves the resources of qubits and avoids the implementation of complex gates, which benefits the experimental platforms in various scenarios. Moreover, this quantum simulation approach can be directly extended to exploring higher dimensional non-Hermitian topological phases and phase transitions.
